Perturb-and-max-product: Sampling and learning in discrete energy-based models

TL;DR

This paper introduces perturb-and-max-product (PMP), a scalable method for sampling and learning in discrete energy-based models, outperforming traditional methods like Gibbs in speed and effectiveness, especially in complex models.

Contribution

The paper proposes PMP, a novel parallel approach for sampling and learning in discrete EBMs built from tractable factors, overcoming limitations of previous linear programming methods.

Findings

PMP is significantly faster than Gibbs and GWG for Ising models.

PMP effectively learns and samples from RBMs.

PMP succeeds in complex models where Gibbs and GWG fail to mix.

Abstract

Perturb-and-MAP offers an elegant approach to approximately sample from a energy-based model (EBM) by computing the maximum-a-posteriori (MAP) configuration of a perturbed version of the model. Sampling in turn enables learning. However, this line of research has been hindered by the general intractability of the MAP computation. Very few works venture outside tractable models, and when they do, they use linear programming approaches, which as we will show, have several limitations. In this work we present perturb-and-max-product (PMP), a parallel and scalable mechanism for sampling and learning in discrete EBMs. Models can be arbitrary as long as they are built using tractable factors. We show that (a) for Ising models, PMP is orders of magnitude faster than Gibbs and Gibbs-with-Gradients (GWG) at learning and generating samples of similar or better quality; (b) PMP is able to learn and sample from RBMs; (c) in a large, entangled graphical model in which Gibbs and GWG fail to mix, PMP succeeds.